If the traffic originated from a wired connection, headed to a wired uplink port, a wireless client couldn't see it, unless they had a packet flooding issue. Wired traffic would be switched, not flooded.
If it was a wireless client originating the traffic, the traffic between the client and the server is still protected with https/TLS, so a wireless snooper could see the site they visited (TLS SNI and/or DNS) and some encrypted payload.
Data at rest on their PC or on a NAS, shared, is another story.